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1 ESSAYS O CORPORATE RISK MAAGEMET AD OPTIMAL HEDGIG CASPER MARTIJ OOSTERHOF

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3 RIJKSUIVERSITEIT GROIGE ESSAYS O CORPORATE RISK MAAGEMET AD OPTIMAL HEDGIG Proefschrift ter verkriging van het doctoraat in de Economische Wetenschappen aan de Riksuniversiteit Groningen op gezag van de Rector Magnificus, dr. F. Zwarts, in het openbaar te verdedigen op dinsdag 9 december 2006 om 4.45 uur door Casper Martin Oosterhof geboren op 5 uni 974 te ieveen

4 Promotores: Prof. Dr. F.M. Tempelaar Prof. Dr. S.Z. Benninga Beoordelingscommissie: Prof. Dr. Dr. h.c. G. Franke Prof. Dr. J. de Haan Prof. Dr. R.H. Koning

5 PREFACE PREFACE Finishing a Ph.D. dissertation is taking a look at the dissertations of colleagues almost equivalent to presenting metaphors, in order to describe the process of completing the study. I will be no exception to this tradition. Thinking back on my (academic and social) life as well as my hobbies and achievements, I would like to relate doing research to a specific area of sports: umping over bars. Economists may call this a very specific subset in the area of sports, which is also the case for doing research on corporate risk management within the broad field of economic sciences. Jumping over 2.5m (or alternatively: 7 feet and inch) without the use of cheating elements like pole vaults, trampolines, or dope, is a process that takes years of training. Credits from the outside world easily go to the one who completes the ob, being either the athlete or in case of a dissertation the Ph.D. student. However, to achieve such a goal in a more or less solitary environment, you need (quite) a little help and support from coaches, family and friends. In the case of athletics: your coach will help you to get better by changing maor and minor details, whereas family and friends support you mentally, when mountains (bars) seem too high to be climbed (umped). The same holds for finishing a Ph.D. thesis: it takes quite a few years of hard effort to finish the document at least for the most of us. Despite the fact that the ob is mainly done by the researcher him- or herself, support and help from others is important or, sometimes, even crucial. Within the academic context of the metaphor, I could never have finished this thesis without the support and inspiration of my supervisors Frans Tempelaar and Simon Benninga. You have both trained me to think about relevant details and see opportunities to extend and improve existing literature, which resulted in the papers that lay the foundation for this dissertation. Without your input, this thesis would never have been finished in the way it is. Furthermore, I would like to thank Günther Franke, Jacob de Haan, and Ruud Koning for willing to participate as a member of my i

6 PREFACE manuscript committee. Your thorough comments and suggestions definitely helped to improve my thesis in the final stages. I also want to thank all my former colleagues at the University of Groningen. Special words of thanks apply to Peter Smid (for getting me interested in doing research during my master s thesis), anne Brunia (for loads of academic- and non-academic-related coffee talks), the secretaries office by means of Diana Kikkert, Janna van Diken, and etty Kempa (for great social interest), and Sebastiaan de Groot (for playing snooker and darts, for pleasant dinners before playing snooker and darts, for the cat, and most importantly for being a friend). Of course, I have also been stimulated by lots of people outside of the academic world. Since I don t want to run the risk of forgetting a single person (I am not as rational as people are assumed in this thesis), I will not name you all. Two of you, however, are quite special to me. I would specifically like to thank Richard van Delden and Frans Peter Posthumus for being great friends during the past, the present, as well as the future (I presume). A special word of thanks applies to the both of you, for willing to perform as an active member during the defense of my thesis. I greatly appreciate that you have accepted my request to become my paranymphs. Henk, Klaase, Albert, and Anita: it is not a lie for me to confess that over the last decade, you have become like family to me. Thank you for the great, more than mental, support. To conclude, I would like to thank the most important people in my life. My dear parents, you have always stimulated me to do whatever I wanted to do. You raised me to the person I am today, by being there whenever I needed you. I truly could not have wished for better parents. Finally, Irma, thank you for the wonderful person you are. During the latest years, you have spent too much time by yourself, because I had to work in the evening and during the weekend. Without your flexibility, moral support, and love, we would not be here today. In the future, I will definitely try to make up the sacrifices you made. Casper ii

7 COTETS COTETS CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO. Introduction.2 Approach and background 4.3 Outline of the thesis 9 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET 3 2. Introduction: Motives for corporate risk management First motive: Reduction of expected taxes Theory Empirical implications Second motive: Reduction of expected costs of financial distress Theory Empirical implications Third motive: Reduction of agency costs of debt Theory Empirical implications Fourth motive: Managerial utility maximization Theory Empirical implications Empirical evidence on corporate risk management activities Introduction Evidence regarding expected taxes Evidence regarding expected costs of financial distress Evidence regarding agency costs of debt Evidence regarding managerial utility maximization Evidence regarding firm size Conclusions 52 iii

8 COTETS CHAPTER 3: HEDGIG WITH FORWARDS AD PUTS I COMPLETE AD ICOMPLETE MARKETS Introduction Unbiasedness of forward and put prices The model Unbiasedness of the forward price Unbiasedness of the put price Joint forward and put unbiasedness Optimal production and hedging by a risk-averse producer Introduction Optimal production and hedging in complete markets Optimal production and hedging in incomplete markets Conclusions 83 CHAPTER 4: THE EFFECT OF MAAGERIAL COMPESATIO O OPTIMAL PRODUCTIO AD HEDGIG WITH FORWARDS AD PUTS Introduction The model Optimal hedging and production with forward contracts Optimal hedging and production with put options Optimal hedging and production decisions Properties of the optimal hedging decisions Conclusions umerical results with respect to put hedging 4.5. Introduction Optimal put hedging in the benchmark case Sensitivity for changes in risk aversion Sensitivity for changes in production Sensitivity for changes in the state prices A oint effect of the parameters Conclusions Conclusions 27 iv

9 COTETS CHAPTER 5: SUMMARY AD COCLUDIG REMARKS Introduction and definitions Summary of the main results Reflection and suggestions for future research 39 SAMEVATTIG I HET EDERLADS 43 BIBLIOGRAPHY 53 v

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11 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO Chapter ITRODUCTIO, BACKGROUD, AD MOTIVATIO. ITRODUCTIO Over the last decades, risk analysis and corporate risk management activities have become very important elements for both financial as well as non-financial corporations. Firms are exposed to different sources of risk, which can be divided into operational risks and financial risks. Operational risks or alternatively business risks relate to the uncertainty regarding the firm s investments and investment opportunities, and are influenced by the product markets in which a firm operates. In addition to operational risks, unexpected changes in e.g. interest rates, exchange rates, and oil prices create financial risks for individual companies. As opposed to operational risks, which influence a specific firm or industry, financial risks are market-wide risks that can affect the financial performance of companies in the whole economy. Both kinds of risk exposure can have substantial impact on the value of a firm. In this context, we define corporate risk management as the process of trying to control the effect of these risk exposures on firm value. Commodity price risk is often considered as a financial risk as well, despite the fact that this is a specific risk exposure for the industry in which a corporation operates. That commodity price risk is usually qualified as a financial risk, is induced by the fact that there exist many derivative instruments in the financial markets with commodity prices as underlying assets. This results in possibilities to efficiently transfer commodity price risk to other market participants.

12 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO There are several reasons to explain why corporate risk management has gained in popularity over the last decades. The most important reason lies in the increased volatility of exchange rates, interest rates, and commodity prices, causing firms cash flows to become more uncertain. Secondly, firms tend to focus more on their core business, which makes them less diversified. As a consequence, the volatility of firms cash flows may increase. A third reason for the growing importance of corporate risk management can be found in the globalization of business activities, in which competition has increased and profit margins have declined. A final explanation we offer is the growing number of opportunities to manage risks. Since the 970s, there have been numerous financial innovations, including new financial products as mortgage-backed securities and derivative instruments such as options and swaps. In addition to these financial innovations, new exchanges for futures, options, and other (complex) derivatives have been introduced and have become maor markets, showing an explosion in trading volume and notional amounts outstanding. As a consequence, risks such as exchange rate risks, interest rate risks as well as commodity price risks can nowadays be transferred quite efficiently among different market participants. Among others, Mason (995) argues that firms engage in corporate risk management through insurance, diversification, and hedging activities. 2 Buying insurance 2 In addition to these possibilities, there are other alternatives to manage risks. For example, a firm s choice of real production activities can also be used in managing risk exposures. By moving production to the country in which products are sold, exposure to exchange rate risk can be decreased dramatically. Furthermore, firm-specific risks can be reduced by geographical diversification, issuing hybrid securities like dual-currency and oil-indexed notes, as well as purchasing insurance. Loss prevention and control, engaging in oint ventures, and the choice of technology, for instance, can all be implemented as a risk management tool for reducing production risks. 2

13 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO contracts implies transferring a risk exposure to an insurance company in exchange for the payment of a premium. Insurance policies are usually employed to manage firm-specific risks like e.g. fire hazards. Diversification means engaging in different business activities that are less than perfectly correlated, thereby reducing the volatility of a firm s cash flows. Hedging a risk exposure is usually done through buying or selling financial derivatives to mitigate the effect of a risk exposure. The standard literature on corporate risk management, which is analyzed in Chapter 2 of this thesis, mainly focuses on the use of financial derivatives within firms risk management programs. In general, derivatives can be used for hedging and speculation purposes. 3 Firms that hedge, use derivatives in order to reduce or eliminate the risks they face from possible adverse changes in certain risk exposures. This is achieved by creating offsetting positions in derivative instruments. Firms that speculate, on the other hand, apply derivatives in order to ) increase the impact of risk exposures on firm value or 2) incorporate their market view into risk management programs. 4 If managers of firms incorporate their personal view in the risk management decision, the total derivatives position may consist of a hedging part and a speculative part. 5 Stulz (996) refers to this type of speculation as selective hedging. In this thesis In addition to hedging and speculation, derivatives can also be used for arbitrage purposes. Arbitrageurs take offsetting positions in different markets or instruments to lock in (risk-free) gains caused by market imperfections. Since arbitrage is usually undertaken by professional financial parties like market makers and hedge funds, in this thesis we abstract from this motivation for the use of derivatives since our focus is on non-financial corporations. Several studies have documented that managers believe that they can create value for the shareholders by incorporating speculative elements into their risk management program (see e.g. Bodnar, Hayt, and Marston, 998). Among others, Stulz (996), Graham and Harvey (200), and Brown, Crabb, and Haushalter (2002) discuss decision making based on market views. 3

14 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO corporate risk management comprises strategies to reduce risk as well as strategies for risk taking. 6 In this dissertation, we concentrate on risk management behavior by nonfinancial corporations, since managing financial risk exposures is not their core business. By managing financial risk exposures, non-financial corporations can focus primarily on business risks, which relate to their core business. In contrast, by dealing in financial securities, financial institutions and financial intermediaries are by definition in the risk management business. Merton (989) even argues that a key feature of financial institutions is to bundle and unbundle different sources of risks. Financial institutions facilitate risk transfers in an increasingly complex area of financial instruments and financial markets; risk management can be seen as a key area of business for financial institutions and intermediaries. As a consequence, their motives for risk management are different from those of non-financial corporations. 7.2 APPROACH AD BACKGROUD The fact that individual firms are increasingly engaged in risk management practices, does not explain why this behavior can be rationalized. Implicitly, the seminal work by Modigliani and Miller (958) lays the foundation for the argument whether or not corporate risk management is relevant. Modigliani and Miller (958) show that, 6 7 Theories of corporate risk management mainly focus on hedging decisions by non-financial corporations. In this thesis, we also provide rationales for why firms may increase risk exposures. Specifically, in Chapter 3 and 4 we show that it may be optimal to overhedge risk exposures. Although a rational decision, this may be qualified as speculation, since the exposure to a specific risk factor is increased at least for certain states of the world. ote that this does not necessarily mean that the firm s net risk exposure is increased. For a discussion on risk management for financial institutions, see e.g. Saunders (997) and Smithson (998). 4

15 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO given complete and frictionless capital markets, the value of a firm is independent of the choice of its capital structure. Based on arbitrage arguments, they show that individual investors can replicate the capital structure exposure of a firm through socalled home-made leveraging or de-leveraging. This analysis can easily be extended to risk management strategies, using similar straightforward arbitrage arguments. If shareholders can costlessly replicate a firm s financial risk management policy ( home-made risk management ), there is no use for firms to do it themselves. 8 As a consequence, from a shareholder s point of view, both the choice of a firm s capital structure as well as its corporate risk management decisions can only matter if capital markets exhibit some sort of imperfection. In a pioneering article, Smith and Stulz (985) provide theoretical rationales for why risk management at the firm level may exist. The demand for risk management by individual firms can be motivated by relaxing some assumptions made by Modigliani and Miller (958). The reasons to engage in risk management at the firm level range from non-linearity of corporate tax rates, to costs of financial distress and agency problems (see Chapter 2). Their approach has been well-accepted in the research on corporate risk management. The theory of the optimal choice under uncertainty has been applied to study risk management decisions from a different point of view (i.e., different from the framework provided by Modigliani and Miller). Central in this line of research is the expected utility theory, introduced by Von eumann and Morgenstern (947). The expected utility theory is a normative model that has dominated the theory of optimal 8 This result holds for all financial decisions. See e.g. Miller and Modigliani (96) for the irrelevance of a firm s dividend policy. 5

16 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO decision making under risk and uncertainty. In this model, risk-averse individual agents maximize the expected value of their utility function. 9 A central and strong element in this line of research is that normative models provide rational procedures for how individual agents should make decisions. 0 Baron (970) and Sandmo (97) are the first to study optimal production under uncertainty, given a risk-averse single owner of a firm, who maximizes a Von eumann-morgenstern utility function. They show that, for higher levels of uncertainty, optimal production decreases. Their models have been extended by e.g., Danthine (978), Holthausen (979), and Feder, Just, and Schmitz (980) to incorporate optimal hedging decisions as well. A famous result is that, when production is non-stochastic, the well-known separation theorem applies. Given the possibility of hedging with unbiased forward contracts, 2 the optimal production decision is independent of the owner s risk preferences and can be separated from the optimal hedging decision. Furthermore, optimal risk management implies full hedging: firms should hedge the price risk of production completely. This model has been extended by numerous research to incorporate e.g. multi-period settings and multiple risk factors, and serves as the basis for our analyses in the Chapters 3 and In fact, utility maximization is more broad. Agents can, of course, also maximize their expected utility under the assumption of risk-seeking behavior or risk neutrality. In the economic literature, however, risk aversion is seen as a key element for the behavior of individual agents. See e.g., Pratt (964) and Arrow (964). Descriptive models, as an alternative, intend to describe how agents make decisions, whether they might be rational or not. See e.g., Kahneman and Tversky (979) and Tversky and Kahneman (986). In this line of literature, the production decision refers to the oint investment and operating activities of a firm. Unbiasedness implies that the current price of a financial contract equals its expected payoff. We will discuss properties of unbiasedness in detail in Chapter 3 of this dissertation. 6

17 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO The theories presented above are designed to explain why risk management at the firm level may be undertaken. Within the theory of corporate finance, firms are assumed to maximize shareholder value, in which managerial risk aversion is unimportant. By imposing market imperfections, such as convex corporate taxes and costs of financial distress, specific costs are introduced for certain states of the world (see Chapter 2). If a firm wishes to avoid these costs, it will behave as if it faces a concave obective function. From this, it follows that the optimization problem for both the framework provided by Modigliani and Miller and the theory of optimal choice under uncertainty can be treated in a similar way. In both cases, the decisionmaker faces a non-linear optimization problem, leading to a rational incentive to decrease the volatility of the firm s cash flows. In the case of utility maximization by a risk-averse manager, the obective function itself is concave, whereas in the case of the approach by Smith and Stulz (985), market imperfections will cause the managers or owners of a firm to behave in a risk-averse manner. The existing literature on optimal risk management policies provides rationales for why individual firms should engage in corporate risk management strategies (see e.g., Smith and Stulz (985) and Chapter 2 of this thesis). That does not answer the question, however, how hedging should take place. Should it be done by selling linear hedging instruments, such as forward contracts or, alternatively, by buying non-linear hedging instruments such as put options? Furthermore, how much should firms hedge? Is it rational to completely hedge certain risk exposures or should firms under- or overhedge? Finally, do operational and hedging decisions interact, and if so, how do they interact? 7

18 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO In this dissertation we mainly build upon the theory of optimal choice in which both optimal production and hedging decisions are analyzed. We have selected this approach because of the strong normative conclusions that can be drawn, in which optimal behavior can be specified. From a theoretical point of view, we provide rational recommendations on the optimal choice of derivative instruments within corporate risk management policies at the firm level. In our analysis, a key issue to explain a rational motive for risk management is the existence of market incompleteness. In this context, capital markets are defined as incomplete if the implicit private pricing systems, which are used by individual economic agents to value financial assets, differ from the equilibrium market pricing systems (i.e., the consensus in the market). In this case, economic agents will, in general, disagree with the market about the pricing of financial instruments. The previous arguments and assumptions are reflected in the main goal of this study: The main goal of this thesis is to extend the existing literature of corporate risk management to provide a better understanding of the interaction between optimal production and risk management decisions through the use of financial derivatives. In order to realize the goal, we define four research questions:. Are optimal production and risk management decisions dependent on the type of derivative contract that can be used for risk management purposes? 8

19 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO 2. Is it rational for firms to engage in full hedging, or should they over- or underhedge total price risk of production? 3. Given the specific type of derivative contract and the optimal amount of production and risk management, is there separation between the optimal production and risk management decision? 4. Do optimal production and risk management decisions change for different kinds of managerial compensation?.3 OUTLIE OF THE THESIS The remainder of this thesis consists of four chapters. 3 The purpose of Chapter 2 is twofold. First of all, it provides a review of the literature regarding the possible rational motives for corporate risk management, which have been briefly introduced in Section.2. Secondly, it serves as a background for the analytical studies in Chapter 3 and 4. It is shown that market imperfections give rise to motives that may induce firms to engage in risk management policies. The impact of market imperfections like exponentially increasing tax rates, costs of financial distress, and agency costs of debt will incur costs for the shareholders that can be eliminated or at least decreased by risk management strategies undertaken at the firm level. Furthermore, since the wealth of managers, which are hired to implement the optimal risk management policy, is often tied to the value and risk of the firm, managerial risk aversion may explain the corporate use of derivative instruments. 3 ote that the structure of this dissertation is essay-based, implying that the individual chapters can be read separately instead of subsequently. Given this structure, relevant definitions and symbols are (re-)defined in each individual chapter. 9

20 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO In Chapter 3, we develop a normative model of optimal corporate hedging and production decisions. In this chapter, we first deal with the market conditions for the unbiasedness of derivative contracts, which is an ever recurring restrictive assumption in the optimal hedging literature. We will show that restricting the probability distribution suffices for unbiasedness to hold and that, therefore, the standard assumption of risk neutrality is too restrictive. 4 Furthermore, we will present the optimal production and hedging decisions of a competitive firm and show that, contrary to previous research, there is a hedging role for put options. Chapter 4 studies the effect of the structure of managerial compensation on optimal production and hedging policies, employed at the firm level. In the financial literature it is widely assumed that managerial compensation through call options gives rise to excessive risk taking since an increase in the volatility of the firm increases the value of managerial stock option holdings. We will show that this is not necessarily true. If the manager is compensated with at-the-money call options, hedging with unbiased forward contracts leads to the same optimal production and hedging decisions as if he were compensated with shares of stock. However, if the manager of the firm can hedge with unbiased put options, optimal production and hedging decisions are not the same if he is compensated with either shares of stock or at-the-money call options. It is optimal to hedge more of the risk exposure and to produce less than in the case of hedging with linear instruments. Chapter 5, finally, concludes and summarizes this dissertation. In this chapter, we review the results from the preceding chapters, discuss the relationships, 4 In the financial literature, unbiasedness is assumed to be possible only in risk-neutral and efficient markets. In Chapter 3 we will show that these conditions are too restrictive. 0

21 CHAPTER : ITRODUCTIO, BACKGROUD, AD MOTIVATIO and describe the contributions of this study to the literature on corporate risk management. Furthermore, we discuss extensions for future research.

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23 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET Chapter 2 A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET * 2. ITRODUCTIO: MOTIVES FOR CORPORATE RISK MAAGEMET Financial risk analysis and corporate risk management are important activities within financial as well as non-financial corporations. Firms are exposed to different sources of business and financial risks (risk exposures), which can affect the value of the firm. Business risks relate to the firm s investments as well as its investment opportunities, whereas financial risks relate to the way these investments are funded. As introduced in Chapter, corporate risk management is defined as the process of trying to influence the effect of these risk exposures on firm value. Managing risk can come in two forms: hedging a risk exposure is the process of trying to reduce the dependence of firm value on this risk exposure, whereas speculation means increasing the dependence on a risk exposure. In this chapter, we will review the literature on the use of derivative securities to alter different risk exposures of a firm, like exposures from exchange rate risk, interest rate risk, or commodity price risk. 5,6 A study by * 5 6 An earlier version of this chapter has been published under the same title as a SOM Research Report in 200. Overall derivatives usage has increased tremendously in recent years. Data obtained from the Bank for International Settlements show that the outstanding amount of OTC-derivatives has increased with 70% from June 200 till June The total notional amount outstanding approximately equals $ 70 trillion in As argued in Chapter, the focus of this chapter is on non-financial corporations. Financial institutions are both users and providers of financial derivatives and could, therefore, face other factors affecting its risk management strategy. For an analysis on the relationship between 3

24 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET Rawls and Smithson (990) shows that financial executives rank corporate risk management as one of their most important obectives, ust behind minimizing borrowing costs and maintaining or improving the firm s credit rating. As this chapter shows, these three obectives are linked. Despite the growing popularity of corporate risk management, there is a broad discussion within the academic literature with respect to the possible contribution of corporate risk management to shareholder value. Under the assumptions of the seminal work by Modigliani and Miller (958), in which they assume a perfect capital market, financial decisions have no impact on the value of a firm. Firm value is created by making profitable investments and the way these investments are financed (i.e., by issuing debt or equity) is completely irrelevant. The financing policy only defines the way in which value is distributed among the different claimants. Central in the Modigliani-Miller framework is the idea that some well-defined assumptions hold. Given perfect capital markets without information asymmetries, absence of taxes (or alternatively absence of discriminatory corporate and personal taxes) as well as non-existence of transaction costs, individual investors are always able to perfectly replicate the financial decisions made by the firm (in the case of Modigliani and Miller (958): the firm s debt/equity decisions). This causes the financial decisions undertaken at the firm level to be completely irrelevant, since individual investors can achieve the same profile by replication, so-called home-made leverage. These irrelevance propositions can be extended to all financing decisions, corporate risk management and firm value for financial institutions, see e.g., Allen and Santomero (998). 4

25 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET like a firm s dividend or risk management policy. 7 Given the same underlying stringent assumptions, then, based on arbitrage arguments, there is no use for corporate risk management in the idealized Modigliani-Miller world. If shareholders want to alter their personal exposure towards certain risks, they can do it on their own, since all financial claims can be replicated perfectly by other financial instruments. Individual investors can therefore achieve the same risk-return profile by so-called home-made hedging. Within the field of corporate finance, it has been recognized from the beginning that the assumptions of the idealized Modigliani-Miller framework are not met in practice. Over the last three decades, many papers have been written about possible motives for risk management practices to be undertaken at the firm level. The rationale behind the existence of corporate risk management is, in the first place, that it adds value to the firm in ways shareholders cannot achieve on their own. If capital markets are perfect in the sense of Fama and Miller (972, p 77), in which ) there are no transactions costs, 2) there is equal access to financial opportunities by firms and individuals, and 3) investors perceive that there are always [perfect CMO] substitutes for any securities of a firm, then individual investors can always replicate the financial decisions undertaken by the firm. Any failure of the critical equal access assumption can lead to a preference for risk management at the firm level over risk management by individuals, implying that the rationale for corporate risk management can be motivated by market imperfections. Relaxing the assumptions made by Modigliani and Miller, therefore, leads to the possible motives for the 7 See e.g., Miller and Modigliani (96) on the irrelevance of a firm s dividend policy. 5

26 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET existence of derivatives within corporate risk management programs since, given these relaxations, individuals cannot replicate the firms financial decisions. For instance, Mayers and Smith (982), Smith and Stulz (985), Smith (995), and Stulz (996) show that hedging can increase firm value for three reasons: ) hedging may add value in case a firm faces a progressive tax rate, 2) hedging may be beneficial when there are expected costs from financial distress, and 3) hedging can effectively mitigate agency problems. These three motives can all be seen in the framework of shareholder value maximization. This implies that, when the underlying market frictions exist, hedging may be a value-increasing strategy for a corporation. As will be shown is this chapter, individual investors cannot achieve these cost reductions themselves leading to a rational reason for risk management to be undertaken at the firm level. A fourth motive for the existence of corporate risk management is of a somewhat different category. Among others, Smith and Stulz (985), Stulz (996), Tufano (996), and Hentschel and Kothari (200) argue that the risk attitude of managers may also explain the use of derivatives within the risk management program of a firm, if a manager s personal wealth depends on firm value. As will be shown in this chapter, when managerial expected utility is a concave function of firm value, managers will be inclined to reduce financial risks by hedging if their future wealth is a linear function of firm value. However, if a manager s future wealth is a convex function of firm value (e.g., when he is rewarded with call options on future firm value), this manager may be inclined to relatively higher risk-taking behavior (less hedging), because a larger volatility of the value of a firm increases his personal wealth. 6

27 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET The value of a firm can be influenced by, for instance, changes in exchange rates, interest rates, or commodity prices. Therefore, a corporate risk manager must understand how the overall risk exposure of a firm is related to the different types of manageable risks. It is very important that the exposures are quantified correctly, otherwise the hedge will lead to an inappropriate result. 8 After the exposures are quantified, the possible hedging instruments must be chosen. In order to hedge the different kinds of risk, firms can rely on a number of derivative instruments like, for instance, forwards, futures, swaps, over-the-counter options, exchange-traded options, structured derivatives, and hybrid debt. As Smith, Smithson, and Wilford (990) show, these so-called building blocks can be combined to construct any desired position which implies that, in theory, any risk exposure can be managed. However, this is only possible under perfect capital markets with rational agents, which is, in practice, not the case. So, in the real world it will be impossible to perfectly hedge every exposure. evertheless, as this chapter will show, the motives for corporate risk management still hold. The purpose of this chapter is to give a critical review of the theoretical motives and determinants for the use of derivative instruments by non-financial corporations. Furthermore, we discuss the empirical findings regarding some important studies. The findings of this chapter will help to determine whether the theoretical motives are indeed observed in practice. The remainder of this chapter is organized as follows. In Section 2.2 it is shown that hedging can increase firm value if firms face a progressive 8 See Stulz and Williamson (997) for an analysis of the identification and quantification of risk exposures. 7

28 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET tax function. Section 2.3 relates to the benefits of hedging in situations of expected costs of financial distress. In addition, Section 2.4 deals with the motive that the corporate use of derivatives can be used to mitigate suboptimal investment policies. The possibility that the risk attitude of managers may explain the use of derivatives in the risk management policy of a firm is analyzed in Section 2.5, after which Section 2.6 contains an overview of some important empirical evidence on corporate risk management. Section 2.7, finally, concludes with a summary. 2.2 FIRST MOTIVE: REDUCTIO OF EXPECTED TAXES 2.2. Theory Among many others, Mayers and Smith (982), Smith and Stulz (985), Rawls and Smithson (990), and Stulz (996) argue that hedging pre-tax income can increase firm value. The line of reasoning is that this will only happen if the firm under consideration is liable to a progressive effective marginal tax rate (implying a convex tax function). 9 The remainder of this section will show that, from the viewpoint of value maximization, hedging can reduce the firm s expected tax liability by decreasing the volatility of its pre-tax income. As a consequence, lowering the expected tax payments increases the present value of the firm. 9 Another tax motive for hedging (at the investor s level) may lie in discrepancies between personal and corporate tax levels (See e.g., Farrar and Selwyn (967) and Brennan (970) for an analysis on the relevance of a firm s dividend policy). In this section, however, we focus on the valueenhancing possibilities of hedging at the level of the firm and abstract from the individual investor who may attempt to maximize his income after taxes. 8

29 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET To illustrate the possible benefits of hedging earnings before taxes, we follow Smith and Stulz (985), and assume a highly stylized one-period model in which there are only two possible future states of the world. The firm s pre-tax income in these two states of the world is given by either or Y. Furthermore, for now assume that the Y 2 firm is an all-equity financed firm. 20 The tax-consequences of hedging for the two possible states of the world are depicted in Figure 2.. The possible states of the world are ordered from bad states to good states. Figure 2.: The effect of hedging on the expected tax payments Tax liability E T U T E [ Y ] H T F [ ] Y Y2 EY Pre-tax income In Figure 2., Y represents the firm s pre-tax income at time if state occurs, whereas Y 2 implies pre-tax income at time, given state 2. The expected income for 20 If the firm is an all-equity financed firm, we can abstract from tax deductions from financing. Tax deductions complicate the analysis, but do not change the result of the advantages of hedging pretax income. See e.g., Smith and Stulz (985). 9

30 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET the firm is given by EY [ ]. The possible corporate tax liabilities are given by the convex dotted line, exhibiting a strictly progressive tax rate. Since the firm is obliged to pay corporate taxes, the expected time- tax liability, given the fact that the firm does not engage in a risk-management policy, is given by E T U, which is the probability-weighted average of the taxes given state and the taxes given state 2. Because the tax schedule is strictly convex the corporate tax amount regarding expected pre-tax income T EY [ ] < E T higher than the taxes regarding expected income. U. The expected corporate taxes are therefore Since the effective corporate tax payments, for the case that the firm does not hedge, are a strictly convex function of pre-tax income, the tax payments disproportionally increase in pre-tax earnings. Therefore, a higher volatility of pre-tax earnings implies higher expected tax payments. To explain this, consider the following situation. If the firm does not hedge, its expected tax liability equals E T, which is the probability-weighted average of the taxes in state and state 2. In the standard literature of finance, the world is usually assumed to be risk-neutral, implying that the prices of derivative instruments are unbiased. Given the possibility of perfect hedging, the manager of a firm can make sure that pre-tax income is equal to U EY [ ] since future income equals expected income given unbiasedness. 2 consequence, the (certain) tax liability for this situation equals convexity of the tax schedule T EY [ ] < E T U T EY [ ] As a. Because of the,22 and firm value increases by the present value of the savings on the tax payments. However, a more realistic view of the 2 22 Unbiasedness of the forward price occurs under risk-neutrality or if restrictions on the probability distribution are assumed. See Benninga and Oosterhof (2004); see also Chapter 3 of this dissertation. This can easily be shown applying Jensen s inequality. 20

31 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET world makes this argument even stronger. If we assume a world of risk-aversion, future certainty-equivalent income will be less than the expected income, that is, [ ] F < E Y. If the firm can make sure that its future income equals F, the certain tax liability will be H T, which is even less than under the assumption of unbiasedness. 23 Summarizing, by hedging the pre-tax income perfectly, firm value will increase by the present value of the reduction in the expected tax liability. Suppose we now turn to a more realistic setting, in which more than two states of the world can occur. Within this setting, if the firm does not hedge, the present value of the expected tax payments { } U E T will be equal to q τ Y, in which q = q, q2,... q is a vector of Arrow-Debreu state prices regarding state, with = {, 2,..., }. 24 τ is a vector of corporate tax rates regarding pre-tax income in state. If the firm is able to create a perfect hedge (i.e., the forward price is unbiased and future income equals EY [ ] ), the present value of the tax payments q H T equals τ Y, where Y is a vector of (certain) income before taxes in case of a perfect hedge. Since this hedge is perfect Y H = τ r f T Y q Since τ Y =, where r + Y = q Y + f = ( r f), it follows that + r f q = Y 25 and, consequently, is defined as the risk-free rate of interest. τ Y = τ q Y. The difference ote that in the standard literature, unbiasedness goes along with risk-neutrality. In Chapter 3 of this dissertation, we will show that this assumption is too restrictive and, restricting the probability distribution, suffices for unbiasedness (see also Benninga and Oosterhof, 2004). The state price regarding state, q, can be defined as the price today, of receiving one currency of payoff in the future, if and only if state occurs. Thus, a state price can be seen as a riskadusted discount factor. Henceforth, a bar will be used to denote a non-random parameter. 2

32 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET between the value of a hedged and an unhedged firm therefore equals q τ Y - τ q Y, which is positive. 26 This implies that, if hedging is perfect and costless, firm value increases by the present value of the reduction in the expected taxes, i.e., q τ Y τ q Y. If hedging is not costless, the difference between the value of a hedged and an unhedged firm will be the maximum amount shareholders are willing to pay for hedging. It should be noted that the hedge does not necessarily have to be perfect in order to increase firm value (i.e., if the hedge is less than perfect, firm value will also increase but less than for the case of a perfect hedge). 27 In this case, the present value of the expected tax liability equals q τ Y, in which Y is a vector of pre-tax incomes when the firm engages in an imperfect hedge. Because hedging reduces uncertainty, is less volatile than and, as a consequence, the expected tax payments will be lower. Therefore, firm value increases by. Thus, given the convexity of the tax schedule and costless hedging, the expected value of the tax liabilities depends on the effectiveness of the hedge, and lies somewhere in between the perfect hedge and the no-hedge case. q τ Y q τ Y Y Y Given the analysis above, it should be clear that hedging can raise firm value if it is possible to reduce the expected amount of tax liabilities. Then the next question might be: How much should a firm hedge?. The preceding analysis implies that, if This is implied by the definition of a concave function. See also footnote 22. In an imperfect hedge, cash flows are still uncertain, but they are less volatile than without hedging. 22

33 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET costless hedging is possible, firms facing a strictly convex tax schedule should hedge all the risk of pre-tax income. This is not necessarily the case when hedging is costly. If the present value of the expected tax reduction is larger than the costs of hedging, firms should also hedge all the risk of pre-tax income. If this is not the case, firms have to look at the marginal trade-off between the reduction in expected taxes and the costs of hedging. Of course, the optimal hedge ratio is calculated by the point where marginal benefits of hedging equal the marginal costs. Thus, if the use of derivatives is not costless, firms hedge ratios should vary between zero and 00% Empirical implications The possible advantages of hedging pre-tax income rely on a number of factors. First of all, the more convex the effective marginal tax schedule, the greater the possible benefits from hedging pre-tax earnings. The convexity of the tax schedule is extended by tax preference items such as investment tax credits, tax loss carrybacks, and tax loss carryforwards. Investment tax credits (ITC s) offset a stated maximum fraction of a corporation s tax liability. The maor effect of ITC s is to shift the effective tax structure down to reflect the value of the tax credit. Tax loss carrybacks and tax loss forwards decrease the tax liability because profits in one year can be offset by losses in another year. This induces the marginal tax schedule to become convex over a larger region, which increases the potential benefits of hedging. Firms with more tax preference items are therefore more likely to hedge their pre-tax income. A second rationale for hedging is that the more volatile the pre-tax income stream, the greater the possible advantages of hedging. Finally, hedging pre-tax income is induced by the probability of encountering in the convex part of the tax schedule. Because small 23

34 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET firms are expected to have lower earnings before taxes, they are more likely to be in the progressive region of the tax schedule. As a consequence, small firms are more likely to hedge pre-tax income. Therefore, it is hypothesized that small firms with tax preference items and a relatively high volatility of income-before-taxes, can be expected to gain most from hedging pre-tax income. With respect to the size of the firm, however, it can be argued that, if the expected gain from hedging pre-tax income depends on transaction costs, larger firms are expected to gain more from hedging because transaction costs usually exhibit economies of scale. Furthermore, and maybe even more important, larger firms are probably in a better position of bearing the costs of setting up a risk management program and contracting capable employees. In this case, larger firms can be expected to enter into hedging activities more often. Thus, theory cannot predict a clear relation between firm size and hedging activities. The empirical evidence on firm size is presented in Subsection SECOD MOTIVE: REDUCTIO OF EXPECTED COSTS OF FIACIAL DISTRESS 2.3. Theory The second motive for hedging at the firm level relates to situations in which there are expected costs of financial distress. Among others, Mayers and Smith (982), Smith and Stulz (985), Froot, Scharfstein, and Stein (993), and ance, Smith, and Smithson (993) show that hedging may increase firm value, given the possibility of financial distress with more importantly costs associated with financial distress. 24

35 CHAPTER 2: A OVERVIEW OF THE LITERATURE O CORPORATE RISK MAAGEMET According to Rawls and Smithson (990), the expected costs of financial distress are driven by two factors: ) the probability of encountering financial distress if the firm does not hedge, and 2) the costs imposed by a possible bankruptcy. These costs can be substantial, not only because of the direct costs of a bankruptcy (e.g., legal costs of lawyers) but especially because of the indirect costs. First of all, suppliers of the firm will offer less attractive payment conditions if a firm is engaged in financial problems. Secondly, signs of financial distress will lead to decreases in sales since this is an indication to customers that service and warranties may cease in the future (loss of reputation). Thirdly, (new) employees will demand higher salaries since they run the risk of losing their ob and, therefore, future income. In order to analyze the value-enhancing effects of hedging with respect to a reduction in the expected costs of financial distress, we again follow Smith and Stulz (985) and assume a one-period model in which there are two possible future states of the world. For simplicity, we abstract from corporate tax payments (i.e., we set τ c = 0 ). 28 Future income in the two states of the world is again given by and Y, in which income Y 2 Y is assumed to be income before direct costs of financial distress. 29 The firm has issued a zero-coupon bond, with a principal equal to B. Furthermore, assume that this debt obligation matures at a single time. At time all cash flows are paid to the different claimants. If income Y is below B, bankruptcy is declared, in which shareholders receive nothing whereas bondholders receive income minus the costs of If we would include taxes in the analysis it would complicate the analysis. However, the basic message will be the same. In fact, shareholder value would increase even further if the firm can, by decreasing the possibility of default, simultaneously increase its debt level. A higher level of debt increases the tax shield and thereby adds to shareholder value. So, the cash flow paid to the claimants will be lower in the case of financial distress, because costs of financial distress have to be paid first. 25